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Step-by-step explanation:
Seja E a expressão que queremos calcular:
The equivalent expression of
is ![\log_c(x^2 - 1) - \log_c(5x)](https://tex.z-dn.net/?f=%5Clog_c%28x%5E2%20-%201%29%20-%20%5Clog_c%285x%29)
<h3>How to determine the equivalent expression?</h3>
The logarithmic expression is given as:
![\log_c(\frac{x^2 - 1}{5x})](https://tex.z-dn.net/?f=%5Clog_c%28%5Cfrac%7Bx%5E2%20-%201%7D%7B5x%7D%29)
The law of logarithm states that:
log(a) - log(b) = log(a/b)
This means that the expression can be split as:
![\log_c(\frac{x^2 - 1}{5x}) = \log_c(x^2 - 1) - \log_c(5x)](https://tex.z-dn.net/?f=%5Clog_c%28%5Cfrac%7Bx%5E2%20-%201%7D%7B5x%7D%29%20%3D%20%5Clog_c%28x%5E2%20-%201%29%20-%20%5Clog_c%285x%29)
Hence, the equivalent expression of
is ![\log_c(x^2 - 1) - \log_c(5x)](https://tex.z-dn.net/?f=%5Clog_c%28x%5E2%20-%201%29%20-%20%5Clog_c%285x%29)
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Answer:
$2.50
Step-by-step explanation: